- 350 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Fourier Integrals in Classical Analysis
About this book
This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.
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Information
Table of contents
- Cover
- Series page
- Title page
- Copyright information
- Dedication
- Table of contents
- Preface to the Second Edition
- Preface to the First Edition
- 0 Background
- 1 Stationary Phase
- 2 Non-homogeneous Oscillatory Integral Operators
- 3 Pseudo-differential Operators
- 4 The Half-wave Operator and Functions of Pseudo-differential Operators
- 5 Lp Estimates of Eigenfunctions
- 6 Fourier Integral Operators
- 7 Propagation of Singularities and Refined Estimates
- 8 Local Smoothing of Fourier Integral Operators
- 9 Kakeya-type Maximal Operators
- Appendix Lagrangian Subspaces of T∗R<sup>n<sup>
- References
- Index of Notation
- Index
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Yes, you can access Fourier Integrals in Classical Analysis by Christopher D. Sogge in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over 1.5 million books available in our catalogue for you to explore.